Advertisements
Advertisements
प्रश्न
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is ______.
पर्याय
1 + 2i
–1 – 2i
2 + i
–1 + 2i
Advertisements
उत्तर
The point represented by the complex number 2 – i is rotated about origin through an angle `pi/2` in the clockwise direction, the new position of point is –1 – 2i.
Explanation:
Given that: z = 2 – i
If z rotated through an angle of `pi/2` about the origin in clockwise direction.
Then the new position = `z.e^(-(pi/2))`
= `(2 - i) e^(-(pi/2))`
= `(2 - i)[cos((-pi)/2) + i sin ((-pi)/2)]`
= (2 – i)(0 – i)
= –1 – 2i
APPEARS IN
संबंधित प्रश्न
Find the multiplicative inverse of the complex number:
4 – 3i
If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`
Simplify the following and express in the form a + ib:
`3 + sqrt(-64)`
Simplify the following and express in the form a + ib:
(2 + 3i)(1 – 4i)
Simplify the following and express in the form a + ib:
`(sqrt(5) + sqrt(3)"i")/(sqrt(5) - sqrt(3)"i")`
Simplify the following and express in the form a + ib:
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Write the conjugates of the following complex number:
`sqrt(2) + sqrt(3)"i"`
Simplify:
`(i^592 + i^590 + i^588 + i^586 + i^584)/(i^582 + i^580 + i^578 + i^576 + i^574)`
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Find the value of x and y which satisfy the following equation (x, y∈R).
(x + 2y) + (2x − 3y)i + 4i = 5
Find the value of x and y which satisfy the following equation (x, y∈R).
`(x+ 1)/(1 + "i") + (y - 1)/(1 - "i")` = i
Select the correct answer from the given alternatives:
If n is an odd positive integer then the value of 1 + (i)2n + (i)4n + (i)6n is :
Answer the following:
Simplify the following and express in the form a + ib:
(2 + 3i)(1 − 4i)
Answer the following:
Simplify the following and express in the form a + ib:
`5/2"i"(-4 - 3"i")`
Answer the following:
Simplify the following and express in the form a + ib:
`(4 + 3"i")/(1 - "i")`
Answer the following:
Solve the following equation for x, y ∈ R:
(4 − 5i)x + (2 + 3i)y = 10 − 7i
Answer the following:
Solve the following equation for x, y ∈ R:
`(x + "i"y)/(2 + 3"i")` = 7 – i
Answer the following:
If x + iy = `("a" + "ib")/("a" - "ib")`, prove that x2 + y2 = 1
Answer the following:
Show that z = `((-1 + sqrt(-3))/2)^3` is a rational number
If |z1| = 1, |z2| = 2, |z3| = 3 and |9z1z2 + 4z1z3 + z2z3| = 12, then the value of |z1 + z2 + z3| is
If z1 = 5 + 3i and z2 = 2 - 4i, then z1 + z2 = ______.
If `(x + iy)^(1/3)` = a + ib, where x, y, a, b ∈ R, show that `x/a - y/b` = –2(a2 + b2)
What is the principal value of amplitude of 1 – i?
If the complex number z = x + iy satisfies the condition |z + 1| = 1, then z lies on ______.
If |z1| = |z2| = ... = |zn| = 1, then show that |z1 + z2 + z3 + ... + zn| = `|1/z_1 + 1/z_2 + 1/z_3 + ... + 1/z_n|`.
The value of `sqrt(-25) xx sqrt(-9)` is ______.
Multiplicative inverse of 1 + i is ______.
If z1 and z2 are complex numbers such that z1 + z2 is a real number, then z2 = ______.
State True or False for the following:
Multiplication of a non-zero complex number by –i rotates the point about origin through a right angle in the anti-clockwise direction.
State True or False for the following:
The locus represented by |z – 1| = |z – i| is a line perpendicular to the join of (1, 0) and (0, 1).
If the least and the largest real values of α, for which the equation z + α|z – 1| + 2i = 0 `("z" ∈ "C" and "i" = sqrt(-1))` has a solution, are p and q respectively; then 4(p2 + q2) is equal to ______.
If `(3 + i)(z + barz) - (2 + i)(z - barz) + 14i` = 0, then `barzz` is equal to ______.
Find the value of `(i^592 + i^590 + i^588 + i^586 + i^584)/ (i^582 + i^580 + i^578 + i^576 + i^574)`
Simplify the following and express in the form a + ib.
`(3i^5 +2i^7 +i^9)/(i^6 +2i^8 +3i^18)`
Simplify the following and express in the form a+ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18`
Simplify the following and express in the form a + ib.
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
Simplify the following and express in the form a + ib.
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
Evaluate the following:
i35
